Question: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 2x - 6$ and $ JT = 9x - 41$ Find $CT$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {2x - 6} = {9x - 41}$ Solve for $x$ $ -7x = -35$ $ x = 5$ Substitute $5$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 2({5}) - 6$ $ JT = 9({5}) - 41$ $ CJ = 10 - 6$ $ JT = 45 - 41$ $ CJ = 4$ $ JT = 4$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {4} + {4}$ $ CT = 8$